A Physicist’s Fresh Look at the ‘Prisoner’s Dilemma’ Reveals Hope for Cooperation

A Rutgers-led study offers a hopeful twist on a classic game theory problem

The "prisoner's dilemma" is one of the most famous ideas in game theory. It even appeared in the Oscar-winning film A Beautiful Mind, which told the story of mathematician John Nash.

For decades, this game has been used to explain why selfishness often beats cooperation.

In the prisoner's dilemma, two players can either cooperate or cheat. Cheating always seems to pay off more, so both players end up cheating and losing out even though working together would have given them the biggest reward.

Scientists have long used this idea to understand everything from microbes sharing resources to human societies negotiating peace. The takeaway message? In the evolutionary race, cheaters win.

A new study led by Rutgers physicist Alexandre Morozov turns that assumption upside down. His research, published in the Proceedings of the National Academy of Sciences, shows that cooperation can emerge naturally without special rules or genetic ties.

"The prisoner's dilemma has told us for 75 years that cheaters always take over in the long run," said Morozov, a professor in the Department of Physics and Astronomy at the Rutgers School of Arts and Sciences. "The end point of any society, based on this, is complete breakdown. But that's not at all the case. Even in a very simple scenario, cheaters don't always win. In fact, it's easier for cooperation to rise."

Morozov and his collaborator, Alexander Feigel of the Hebrew University of Jerusalem, discovered that the key to cooperation is keeping track of your opponents. If individuals can recognize others, cooperation starts to flourish.

"All you have to do is remember who you interacted with and react in the same way," said Morozov, who is also director of the Rutgers Center for Quantitative Biology. "That's enough for cooperation to emerge by itself in many scenarios. It's what physicists call an emergent property."

This finding is striking because previous theories required extra conditions such as helping relatives or sticking with your group. Morozov's model works without those assumptions. It suggests that, even in simple organisms such as microbes or insects, cooperation can evolve if these organisms are able to tell each other apart, perhaps through chemical signals or physical traits.

Game theory underpins this research. A game, in the mathematical sense, is a situation in which players make rational decisions according to defined rules to receive some sort of payoff. Game theory is the branch of mathematics that studies these interactions and helps explain why strategies such as cooperation or cheating emerge in nature and society.

Cooperation is the foundation of complex life, Morozov said. Without it, cells wouldn't form tissues and societies wouldn't exist. Yet Darwinian evolution seems to favor selfishness. Morozov's work offers a new way of understanding how life overcame that hurdle.

"Evolution likes shaping things over long periods of time if it has some material to work with," Morozov said. "If cooperation always dies off, there's nothing to evolve. But if there's a chance, evolution will refine it and make it more stable."

The implications go beyond biology. Morozov said that his model shows periods of stability interrupted by upheaval, patterns that might sound familiar in human history.

"Cheaters don't always win," he said. "Cooperation can persist, and it does persist in many systems scientists look at, such as multi-cellular organisms in which individual cells have to cooperate to survive."

Morozov started his career as a physicist focusing on protein folding and statistical mechanics, which deals with predicting the behavior of complex systems. Later, he realized those same mathematical tools could help explain how living things evolve. For years, he has explored evolutionary dynamics, building models that show how traits spread in populations under evolutionary forces such as mutation and natural selection.

That experience, Morozov said, gave him the foundation for his latest work. When he encountered game theory during a sabbatical at the Hebrew University, he saw a connection. The same methods he used to study molecules and genes, he realized, could also reveal why cooperation, rather than selfishness, sometimes wins in the prisoner's dilemma.

The team used mathematical models and computer simulations, including populations of neural networks playing repeated games. A neural network is a computer system modeled after the human brain that teaches patterns and makes predictions by processing information through layers of interconnected nodes.

The scientists also produced a new theoretical result, a generalization of a classic evolutionary principle called Fisher's fundamental theorem of natural selection.

Morozov said he hopes the work will spark new research on how cooperation evolves in nature and maybe even inspire fresh thinking about cooperation in human societies.

Explore more of the ways Rutgers research is shaping the future.